Adam Dell has won his bitter battle with “Top Chef” host Padma Lakshmi over their daughter, Krishna. The wealthy venture capitalist has succeeded in being recognized as Krishna’s father, and now the 2-year-old child will carry his famous last name.

Sources said after settling their fight over the baby, the tot will now be known as Krishna Thea Lakshmi-Dell. And Adam — brother of computer king Michael Dell — has also secured extra custody and visitation rights to the baby girl.

Dell sued Lakshmi in Manhattan Supreme Court last year, claiming she had refused to put his name on the birth certificate, and had cruelly told him she hoped her late partner, billionaire Teddy Forstmann, “was the child’s biological father.”

He also said in court papers that Lakshmi pushed him into signing a restrictive temporary visitation agreement that only gave him a few hours a week with the girl, while encouraging the child to call Forstmann “Papa.”

But DNA tests taken while Lakshmi was still pregnant proved her father was Dell, who then demanded full custody and sued to get Krishna’s name changed.

A source told us, “Their dispute was settled privately, out of court. Dell got improved visitation and custody rights. He had wanted full custody, but they came to a compromise. Padma maintains the same rights she always had.”

Another source told us that Dell “adores this little girl more than anything else, and just wanted to make sure he could be a huge part of her life.” IMG boss Forstmann died last November, leaving an undisclosed sum in trust to Krishna.

A rep for Lakshmi told us, “Officially we have no comment, but as Krishna’s mother, Padma asks that her child’s privacy be respected and the media shift their attention elsewhere.” Dell’s lawyer, William Zabel, declined to comment.